Democratic Caucus Chairman Xavier Becerra, D-Calif., is among the House Democrats supporting the 9/11 bill while expressing concern it could open up the United States to new litigation abroad. (Photo By Bill Clark/CQ Roll Call)

House Democrats on Wednesday further offered their support for a bill that would allow victims of the Sept. 11 terror attacks to take legal action against foreign countries while acknowledging President Barack Obama’s opposition.

Rep. Joseph Crowley, a New York Democrat, said he understood Obama’s concerns the bill could open the door for other nations to tie up the U.S. government in costly and lengthy litigation abroad.

But Crowley reiterated the notion that families of victims of the attacks should be given the authority to take legal action if a foreign entity is found to be connected to a terror attack on U.S. soil. Crowley said he supported the legislation.

“I believe that justice is paramount and having an opportunity to find the truth is paramount wherever that may lead," Crowley said, adding he would wait to see the president’s anticipated veto message and then “take it from there.”

White House Press Secretary Josh Earnest on Tuesday evening reiterated that Obama will veto the legislation. He did, however, acknowledge the White House has "a steep hill to climb to address the concerns that we have raised about this legislation."

"Members of Congress in both parties have indicated that they are open to the concerns that we've expressed -- in many cases, they share them," Earnest said. "And the real question for members of Congress will be whether or not they're prepared to cast a vote that is consistent with the views and feelings that they express in private."

The measure passed with overwhelming bipartisan majorities in both the House and Senate. But a roll call vote in the House could present a sticky political situation for members who have legal issues with the bill but worry about appearing not to support terror victims' families.

Democrats avoided addressing the political ramifications of such a scenario.

Rep. Xavier Becerra, a California Democrat, expressed support for the bill but echoed Obama’s concern that it could also open Americans up to litigation in foreign courts.

“I would rather be in our courts than the courts of a lot of other countries,” Becerra said.

“Many of us are prepared to vote for it understanding that the sovereign immunity principle, which could impact us in the future could have some results that we don’t like,” Becerra said.

Speaker Paul D. Ryan, R-Wis., also said on Wednesday he had concerns but again predicted the House would override a veto.

"I worry about legal matters. I worry about trial lawyers trying to get rich off this and I worry about the precedence," Ryan said. "At the same time, these victims need to have their day in court."

Ryan said the House would take up and pass a veto override if and when it passes the Senate this month.